Planck's quantum theory and photoelectric effect

Classical wave theory failed for black-body radiation, the photoelectric effect, the heat capacity of solids at different temperatures and the line spectra of atoms.

A black body is an ideal absorber and emitter of all frequencies; its emission depends only on temperature. Intensity rises with wavelength to a peak and then falls, and the peak moves to shorter wavelength as temperature rises, which is why heated iron glows dull red, then brighter red, then white and then blue.

Planck (1900): energy is emitted or absorbed only in packets called quanta, with E = hν and h = 6.626 × 10⁻³⁴ J s. Allowed energies are 0, hν, 2hν, 3hν … and nothing in between, like standing on steps of a staircase.

Photoelectric effect (Hertz, 1887): light ejects electrons from metals such as potassium, rubidium and caesium. Ejection is instant, the number of electrons grows with brightness, and below a threshold frequency ν₀ no electron comes out at any brightness.

Einstein (1905): light is a stream of photons; one photon gives all its energy to one electron. Energy balance: hν = hν₀ + ½mₑv², where hν₀ = W₀, the work function.

Above the threshold, the kinetic energy of the electrons rises with frequency and does not depend on brightness; brighter light only means more photons and so more electrons.

NCERT's work functions (eV): Li 2.42, Na 2.3, K 2.25, Mg 3.7, Cu 4.8, Ag 4.3. NCERT's text also quotes the threshold for potassium as 5.0 × 10¹⁴ Hz, so in a numerical use the value the question gives.

Light is dual: it shows wave behaviour (interference, diffraction) while travelling and particle behaviour when it interacts with matter.